The particular topic is the general notion of whether mathematics, and similar sorts of activities, are describing something that is real. I have touched upon this topic in previous posts. In some ways, this argument is at the very heart of the worldviews that assert there can be some absolute truth, moral principles, authority, etc. You can't hang an absolute morality or absolute knowledge on a logical foundation that is arbitrary, at least not without some cognitive discomfort.
So, n Anderson's post on mathematics, we find Anderson arguing for how mathematicians feel mathematics is a feature of reality. All quotes following are from his post, unless otherwise noted.
Mathematics is also a very interesting field if you have an interest in philosophy and questions about design in nature. Almost all mathematicians are in practice realists - they believe that as they make progress in their field they are involved in discovering and not in inventing. (See here for more on this distinction). That is, they act and research as if there is already a transcendent, pre-existing mathematical universe "out there" that is waiting for us to find and explore it. The opposite of that is behaving as if mathematics is our arbitrary toy, to be played with, deconstructed and rebuilt as we please. Shall we adopt the convention that 2+2 = 5 from now on and see where that takes us?
Yes, the good old 2+2 = 5 argument (it never occurs to such people that it is perfectly reasonable in some circumstances to say 2 + 2 = 1). Now, I am sure there are mathematicians who think there is some big design they are uncovering, and that belief does not prevent them from being fine mathematicians. It's probably even a positive when you are working closely with computer scientists, engineers, or physicist in pushing the boundaries of mathematics for direct applications. However, having enjoyed some 66 semester hours of undergraduate mathematics and another 36 at the graduate level, I can say that I ran into more than a few instructors and fellow students who treated mathematics exactly like an arbitrary toy, something you could play with, take apart, and build to order. Most of them, to my knowledge, would not have cared if there were a philosophical position that reflected this attitude, but I find fictionalism to be a decent approximation. We were playing in a universe we created for our benefit, and occasionally something useful would pop out.
In my view, the atheist materialists who have tried to explain their view of reality are in an exceptionally weak position when they seek to explain mathematics in non-transcendent terms. Mathematics resists, at multiple levels, any attempt to treat it as an arbitrary invention of the human mind. Almost at every turn it cries out "I was here before you, and I am bigger than you!". Maths is a very theistic subject!
Actually, mathematics is highly receptive to humans treating it like an arbitrary invention. It's why we have Euclidean, Lobachevkian, and Riemannian geometries to describe different sorts of space. It's we we have intuitionist, constructivist, and para-consistent logics and their mathematical descendants. We add or remove axioms at our pleasure, look at the results, and call it fun (and occasionally useful).
I can of course always add two apples to two apples and will always get four apples (an inconvenient truth for the atheists who want to argue that mathematical truths are not transcendent!) - but as I do so I'm conscious that there is a notion of "two-ness" or "four-ness" that goes far beyond the tasty bits of fruit and is independent of them.
Now, this is a great example of fuzzy-headed thinking, an absolute truth that is right except where it is wrong. If I smash two apples against two apples, I will quite possibly have over 100 bits of apple. If I pour two liters of water into two liters of alcohol, I will have under 3.9 liters of fluid. Except in very limited circumstances, numbers are not conserved!
The more complicated the mathematics gets, the more obvious this becomes. I can move from the simple adding of objects to a dimension up and do calculus to work out the area under a graph. I can then accelerate to five or six dimensional spaces and work out their corresponding concept of volume. I can work out the properties of completely theoretical objects. you get the idea. Mathematics speaks to us of an ideal reality which depends on the mind.
Here's an interesting question: how the fundamental nature of an ideal reality depend upon a human mind? Personally, I don't think is can or does. Perhaps Anderson mistyped, and meant that the reality is revealed to the mind, or perhaps it was a Freudian slip. I do think that the reality of any particular five-dimensional construction we create depends on our mind. That makes it not a fundamental property of nature.
Whilst it depends on the mind, mathematics also seems to have an unbreakable link to the physical world. In the most simple example, there's something about those two oranges that has the notion of two-ness. The notion of two-ness is contained, but not exhausted, by them.
The notion of twoness, and similar notions, is the pattern that we humans impose upon our world to make it simpler. Since we are identifying a pattern, it is unsurprising that no one instance of the pattern will form a complete rendition.
I can create a two-dimensional shape that is approximately (but never exactly - because we live in a world of discrete atoms and molecules) equal to the one in the equation of the graph I was using. This is all simple enough.
Anderson references quantum mechanics later on. Perhaps it's my ignorance, but wouldn't it be much more correct to say we live in a worlds of fuzzy atoms and molecules behaving in probabilistic ways? Even here, the need to have absolutes alters the mindset.
What is more breath-taking, though, is to understand that correspondences between abstract mathematics and the physical world have also been discovered in far more complicated cases. In some areas, mathematicians discovered new theorems in highly abstract areas that nobody thought would ever turn out to have a practical application - but in fact they actually perfectly described physical phenomena observed decades later. Do you get that? Away in his dusty study somewhere, the mathematician was working on a problem that was thought to be far too abstract to have any real application. Some time later, a physicist realised that this bit of mathematics was the key to something that he was observing. Quantum physics provides a number of illustrations of this.
I'm not sure why this is particularly breathtaking. While we play with mathematics as a toy, we also do like to make it useful. So, a mathematician, playing around with equations that are useful descriptions of quantum mechanics, comes across a new feature which also has utility, based upon deductively playing with something already utilized. I don't see why that would be surprising. I don't think it would be particularly shocking to Anderson if an engineer predicted that a steel beam would collapse under a certain weight load, and was correct.
Observation one: Mathematics has its seat in minds. Observation two: We also now know that mathematics is also embedded at a fundamental and essential in physical reality. Inescapable conclusion: Physical reality is the product of a mind.
Anderson very obligingly illustrated my point for me. This notion of real versus useful fictions is not just semantics and playing with words. It's a part of how and why believers believe, one of the pillars they use to prop up their world view.
I'll offer one final link to a rant by a mathematician, offered because he views mathematics as an art. I don't endorse everything he says about education, but his view of mathematics fits much more closely with the mathematicians I learned from and with.
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65 comments:
One Brow said: "Anderson very obligingly illustrated my point for me. This notion of real versus useful fictions is not just semantics and playing with words. It's a part of how and why believers believe, one of the pillars they use to prop up their world view."
An obvious formist (Platontist) in Pepper's classification of world views, eh, Eric? The argument that number are real entities which (pre-)exist independently of our "discovery" of them seems self-evident to many people, and is one that convinces many thinking people that platonic idealism has undeniable merit.
Like you, I don't buy this view, but it does raise the same interesting kinda questions concerning how directly and faithfully the interaction of sense perception and mental constructs "truly" correspond to the external world that we have been touching on in the evolution thread.
I really don't understand how you can see math as a simply a human mental construct and yet believe that "theories" can be tantamount to "fact," truth be told.
I really don't understand how you can see math as a simply a human mental construct and yet believe that "theories" can be tantamount to "fact," truth be told.
Because, mcuh like a scientific fact is in a different category from a scientific theory, I see a mathematical theory as being in a different category from a scientific theory.
One Brow said: "Because, mcuh like a scientific fact is in a different category from a scientific theory, I see a mathematical theory as being in a different category from a scientific theory."
Well, I'm not sure how you can distinguish a "scientific fact" from a mere fact fact. I would agree that it is a fact that if I stick this uninsulated screwdriver into that electrical socket, it will shock the piss outta me. I also realize there are theoretical explanations for electricity involving the flow of electrons complete with "laws" about ohms, amps, volts, etc.
Does that make it a "scientific fact" that it will shock the piss outta me? Will the shock be any different, with or without the theory?
Euclidean plane geometry may be a formal deductive system, but the pythagorean theorem helped build the pyramids. If, for example, you have 3 pieces of rope, one of which is 3 feet, one 4, and one 5 feet long, and you connect the 3, end-to-end, in such a way as to enclose an area, one of those angles will be a 90 degree angle.
I'm not sure the egyptians had a "theory" to explain this correspondence, but they didn't need a theory for it to work. It simply works that way, theory, or no theory, and even though the "science" of civil engineering is different from the "science" of mathematics.
Well, I'm not sure how you can distinguish a "scientific fact" from a mere fact fact.
Well, I was not really trying to make that distinction. However, I will say that many people will refer to '2 + 2 4' as being fact, and their salvation by Jesus as being fact. I would consider those propositions as different types of facts from each other and from scientiic facts. The three are arrived at by different means, for one thing (deduction vs. induction vs. revelation). I don't think that distinction is relevant to our discussion.
Does that make it a "scientific fact" that it will shock the piss outta me? Will the shock be any different, with or without the theory?
Yes, and no.
Euclidean plane geometry may be a formal deductive system, but the pythagorean theorem helped build the pyramids. ... I'm not sure the egyptians had a "theory" to explain this correspondence,
Formal systems are not chosen for thoeries on how they apply, they are chosen for usefulness or general interest. Euclid chose his axioms because he thought they would work. I tell my students that formal systems are like models of a building. You can build a model any way you want, but if you want to use teh model to examine the building, you make it resemble the building as closely as possible. However, you can't judge the usefulness of a model just by looking at the model, in the same way the formal system is only as useful as its correspondance to reality.
Formal systems are different from scientific theories, of course, but in many (perhaps most) ways, they are also very similar.
The main, obvious, difference is, of course, the subject matter. Math deals with abstraction and definitions, not objects found in the world. That 2 + 2 = 4 is "absolutely" true within in a math framework because it is in essence a matter of definition (form, hence the "formal" designation). The conclusions implied by a formal system, at least if it is consistent, coherent, etc., will necessarrily be "true" within that system, even if they contradict observed "reality."
Other than that, both math and science are based on logic (itself a formal system). If you take a particular branch of math, say the one dealing with statistics, you can derive all kinds of formulae which serve to summarize a portion on the necessarily implied conclusions generated by the premises, and use them to calculate "probabilities."
When you ask how statistics correspond to the "real world," the only answer you can give is that the theories will apply in (or correspond to) the world to the extent, if any, that the world actually conforms to the premises used to deduce the formulae. This, of course, is not always (or, more accurately, never) known.
Scientific theories are no different in this respect. The same question has the same answer: the implications and conclusions of scientific theory will apply in (or correspond to) the world to the extent, if any, that the world actually conforms to the premises used to deduce them.
As I argued in the other thread, if a necessary conclusion does NOT conform to the real world, that does not, and cannot, change the either validity of a deduction or the content of the premises which generated it, and that is true whether you're dealing in science or pure math. In that case, with math, you simply say "So what?" With science, you say the theory has been falsified.
In other words, because the subject matter of formal systems is different than that of (pure) math, so are the practical goals. Math is only concerned with the validity of it's logical conclusions. Science is concerned with both the validity of its logical conclusions, and the soundness of the premises from which they are derived. Neither one can say with certainty that their premises correspond to the real world, it's just that (pure) math doesn't even care.
Edit: Meant to say: In other words, because the subject matter of scientific theories [not "formal systems"] is different
Formal systems are different from scientific theories, of course, but in many (perhaps most) ways, they are also very similar.
They differ in their motivation for choosing starting points (inductive leaps based upon experimental observations vs. basically arbitrary selections based upon perceived usefulness or other interesting aspects). They differ in the methods of demonstrating the results of the system (experimental validations in untested situations vs. follow a specific calculus in a precise fashion to a desired outcome). They differ in regard to the level of certainty accorded results (every result is provisional vs. absolute certainty).
The main, obvious, difference is, of course, the subject matter. Math deals with abstraction and definitions, not objects found in the world.
That another difference, but possibly not even as important as the three I just mentioned.
... the only answer you can give is that the [formal] theories will apply in (or correspond to) the world to the extent, if any, that the world actually conforms to the premises used to deduce the formulae. This, of course, is not always (or, more accurately, never) known.
I agree.
Scientific theories are no different in this respect.
I disagree. We already know the starting assumptions of the scientific theory apply to the real world, or at least in a limited environment therein, because this is where they originate. While we can never be certain of their accuracy, the gap that comes from reliance on an inductive process is different qualitatively from the gap that comes from an arbitrary selection process. That's why, as knowledge about the environment gets added to, scientific theories incorporate and change instead of die and resurrect in an altered form. Science is never certain, but it is always about the real world.
The same question has the same answer: the implications and conclusions of scientific theory will apply in (or correspond to) the world to the extent, if any, that the world actually conforms to the premises used to deduce them.
As long as you treat the conclusion of an inductive process as being indistinguishable from the arbitrary selection of a starting point, you won't see much difference between science and formal systems.
As I argued in the other thread, if a necessary conclusion does NOT conform to the real world, ... With science, you say the theory has been falsified.
In science, you are much more likely to alter a theory than falsify it. Hypotheses get falsified frequently, but theories will already have been so validated that new information is more likely to produce an accomodation.
In other words, because the subject matter of scientific theories is different than that of (pure) math, so are the practical goals. Math is only concerned with the validity of it's logical conclusions.
Math has other concerns, as well.
Science is concerned with both the validity of its logical conclusions, and the soundness of the premises from which they are derived. Neither one can say with certainty that their premises correspond to the real world, it's just that (pure) math doesn't even care.
Many mathematicians would disagree. They are interested in producing results that can be used by businesses, scientists, etc.
I said: "The main, obvious, difference is, of course, the subject matter. Math deals with abstraction and definitions, not objects found in the world.
You responded: "That another difference, but possibly not even as important as the three I just mentioned." [the other three bein certainty, demonstration, and motivation for choosing premises].
I later added: "In other words, because the subject matter of formal systems is different than that of (pure) math, so are the practical goals."
I still see the nature of the subject matter as being fundamental, with the things you mentioned simply being a by-product of that difference. As I read Gould, he is saying that "scientific theories" (which are "structures of ideas") differ from "facts' (the world's data), in just the same way that mathematical theorems differ from "facts," and I agree.
Neither math nor scientific theory can be sure that their chosen premises correspond to the real world. Both often attempt to do so test correspondence, however. "Applied math" makes the attempt to achieve correspondence, just as general scientific theory does. Think of Kepler's laws of motion or Newton's law of gravity, which simply strove to summarize perceived regularities of nature via symbolic mathematical form.
Like I said, pure math need not concern itself with soundness (in terms of correspondence to reality), but applied or practical math does. Math is basically a deductive tool used to aid scientific theory in it's deductive processes. After the premises are posited, whether in math or scientific theory, the process is basically deductive thereafter.
Math conclusions are no more "certain" than those of science, insofar as certainty about they apply to the world. They are only "certain" in the sense that tautologies are. A is A, it's just that simple. The ultimate metaphysical assumptions of both math and science are the laws of logic (identity, non-contradiction, and excluded middle).
One Brow said: "Many mathematicians would disagree. They are interested in producing results that can be used by businesses, scientists, etc."
Yeah, I agree, which is why I used the modifier "pure" in some of my references to math. This is also why the premises of most formal systems (Euclidean geometry, for example) are not simply "arbitrary." I can posit purely arbitrary premises for use in a scientific theory, and the same can be done with math, but what good would that be?
One Brow said: "I disagree. We already know the starting assumptions of the scientific theory apply to the real world, or at least in a limited environment therein, because this is where they originate."
I am using the phrase "apply to" differently than you are in this statment. I basically used "apply to" as bein synonymous with "correspond to." I also think it is a mistake to assert that scientific premises "originate" in the real world. They "originate" in the brain (which is presumably part of the "real world," but, still....).
That is why I said I found it somewhat surprising that you are a nominalist (fictionalist, if you prefer) with respect to numbers, but basically a "realist" when it comes to scientific theories. If numbers are not "really" in the world, then certainly scientific hypotheses are not "in the world."
One Brow said: " Hypotheses get falsified frequently, but theories will already have been so validated that new information is more likely to produce an accomodation."
Well, that's why I originally pressed you about what, exactly, what you call the theory of evolution consists of. If the basic "theory" is merely that "evolution occurred," then that broad premise will be capable of "accomodating" any given hypothesis which is not "evolution did not occur."
From what (little) I read on message boards where evolutionists debate "creationists," there is a great deal of equivocation pertaining to the term "evolution," but the combatants often treat "the theory of evolution" as simply asserting that evolution occurred. That is one acceptable use of the term "theory," but it is not a "scientific theory," by any means.
I still see the nature of the subject matter as being fundamental, with the things you mentioned simply being a by-product of that difference.
I would submit that is it passible to create a genuinely formal theory regarding reality, but it will still suffer from the strengths and weaknesses of a formal theory, as opposed to those of a scientific theory.
Neither math nor scientific theory can be sure that their chosen premises correspond to the real world.
Scientific theories do correspond to a limited part of the world. Their inaccuracy comes from an insuffient understanding of other parts of the world. Foraml theories do not have a guarantee of correspondence to any part of the world.
Think of Kepler's laws of motion or Newton's law of gravity, which simply strove to summarize perceived regularities of nature via symbolic mathematical form.
The impetus for these laws is establishing a correspondence to real events.
Math conclusions are no more "certain" than those of science, insofar as certainty about they apply to the world. They are only "certain" in the sense that tautologies are.
I would say they are far less certain to apply to reality, since reality is not used internally in a formal theory.
The ultimate metaphysical assumptions of both math and science are the laws of logic (identity, non-contradiction, and excluded middle).
Science does not require non-contradiciton nor the excluded middle to operate.
I can posit purely arbitrary premises for use in a scientific theory, and the same can be done with math, but what good would that be?
In math, you can do it for the pleasure or artistic merit. In science, positing arbitrary premises is not doing science at all.
I am using the phrase "apply to" differently than you are in this statment. I basically used "apply to" as bein synonymous with "correspond to."
As was I.
I also think it is a mistake to assert that scientific premises "originate" in the real world. They "originate" in the brain (which is presumably part of the "real world," but, still....).
They orginate in experiemental results, which are processed by inductive leaps in the brain.
If numbers are not "really" in the world, then certainly scientific hypotheses are not "in the world."
I disagree, based on how they originate.
Well, that's why I originally pressed you about what, exactly, what you call the theory of evolution consists of. If the basic "theory" is merely that "evolution occurred," then that broad premise will be capable of "accomodating" any given hypothesis which is not "evolution did not occur."
'Evolution occured' is not the type of knowledge that can be a hypothesis or theory.
From what (little) I read on message boards where evolutionists debate "creationists," there is a great deal of equivocation pertaining to the term "evolution," but the combatants often treat "the theory of evolution" as simply asserting that evolution occurred. That is one acceptable use of the term "theory," but it is not a "scientific theory," by any means.
Well, creationists often dispute the fact of evolution as well as the theory, and not every person has thought out the difference between them to the degree we are trying to do.
One Brow said: "I would submit that is it passible to create a genuinely formal theory regarding reality, but it will still suffer from the strengths and weaknesses of a formal theory, as opposed to those of a scientific theory."
You have some vague (to me) notion of what a "scientific theory" is. Do you see a "scientific theory" as being any kinda thought (which one might call "theoretical") about the objects of the world?
I said: "If numbers are not "really" in the world, then certainly scientific hypotheses are not "in the world."
You responded: I disagree, based on how they originate...They orginate in experiemental results, which are processed by inductive leaps in the brain.
If you think that thoughts (inductive leaps) "originate" in experimental results, then it seems that you would have to agree that numbers "originate" in sense data too. We formulate the notion of "2" after first seeing 2 cows, then 2 pigs, etc., and then "processing" that data and abstracting the theoretical notion of 2. The numeral 2 is therefore in, and comes from, the world, not our brains.
Really, Eric, I think you are trying to make a distinction here that would be impossible to consistently to apply in such a way as to distinguish math theory from theory in the empircal sciences. You are arguing exactly the way a Platonist would for the "reality of," and the "origination of" numbers.
One Brow said: "Science does not require non-contradiciton nor the excluded middle to operate."
Which is the same as saying the laws of logic are not required. Again, I don't know what you mean by the word "science" here. Certainly it does not require logic to simply observe, if that's what you are callin "science." I am just talking about "scientific theory" here (the theoretical aspect of "science"), not the whole range of activities that one might legitimately include under the general rubric of "science."
Without the strict application of logic, "scientific theory," at least in the sense that the wiki entry we reviewed defines and explains it, cannot exist. You might have "mystical" or "intuitive" theories without logic, but not "scientific theories."
I would agree that the inspiration for a novel scientific hypothesis might be called "intuitive," but not the process of "testing" it by trying to confirm that what it predicts is consistently with what we observe.
One Brow said: "'Evolution occured' is not the type of knowledge that can be a hypothesis or theory."
Why not? I can't see it as anything but a hypothesis. It is not a full-blown "scientific theory," of course, but nor is it a "fact" which you can observe. It is a mental contruct. We can't see gravity--it too is an abstract notion. If I'm not mistaken, the word "gravity" (for "heaviness) was coined by the greeks. They had four elements (earth, wind, fire, and water). Aristotle later added a fifth one (aether) for the immutable, uncorruptible "heavenly" substance. Earth had "gravity;" it would displace and sink to the bottom of water, and always "sought" it's place at the bottom (beginning) of things. Air (wind) and fire did not have gravity. Their tendency was to rise, seeking hiher places.
This is all theoretical, of course, but the point is that the word "gravity" was simply coined (as were the words "two" and "three") to represent an abstaction made from observation. But "gravity" is no more tangible than is the concept of the numeral 2. Neither comes from sense perception, per se, unless you are a Platonist, mebbe.
I seen Natural Selection down at Red's Road House last week, and, lemme tellya, that dude looked a little rough around the edges, know what I'm sayin? He hadn't shaved for a least a week, he was tryin to panhandle money for a ham sandwich and some liquor, and he really stunk.
I said to him, I sez: Zup, there, eh, Natz?"
He sez: "Sheeit, thangs aint so good no mo. I done lost my job, ya know? Seems lotta them scientists don't like my work so good no more. Imma make a come-back, here soon, though, just you hide and watch."
One experiment, among many similar ones, done with children goes like this:
A kid is shown two containers with water in them. One is a large-diameter, mug-shaped container, and the other is a narrow conical or cylindrical shape, like a test tube, for example. Both are on a table, and the water level is about 1 inch above the table top for the liquid in the mug, and the liquid in the tube is about 10" above the table top. Git the picture?
The kid (say around 4 years old) is then asked which container has more water in it. Children will invariably say the tube does (even though the amounts are in fact identical).
Then they empty one of the containers, say the tube. Then they pour the water from the mug into the tube, and ask again which one had (or has) more water in it. The kid still says the tube does. They can pour the water back and forth from one container to the other dozens of times, and the kid will always say the tube has (or had) more water in it than the mug.
Of course it is the same water, and it cannot be more or less than itself. That's just the old law of identity, right? Why can't the kid "see" this? Mebbe because the concept of "identity" is not an empirical one, cannot be seen, and is not "in" the water, at least not in any observable sense, whaddaya think?
One Brow said: "Scientific theories do correspond to a limited part of the world. Their inaccuracy comes from an insuffient understanding of other parts of the world. Foraml theories do not have a guarantee of correspondence to any part of the world."
I gather that you are suggesting that scientific theories DO have a guarantee of correspondence to at least some part of the world. Are you somehow equating sense perception (one form of "fact") with scientific theory, thereby denying Gould's distinction?
Here is a relatively brief article about the history of epistemological thought. Here are a couple of excerpts: "From the 17th to the late 19th century, the main issue in epistemology was reasoning versus sense perception in acquiring knowledge....In the early 20th century...special attention was given to the relation between the act of perceiving something, the object directly perceived, and the thing that can be said to be known as a result of the perception....British philosopher John Langshaw Austin argued, for example, that to say a statement was true added nothing to the statement except a promise by the speaker or writer."
http://encarta.msn.com/encyclopedia_761573017/epistemology.html
Is your sense that scientific theories "guarantee" a measure of correspondence to reality really just your "promise," ya figure?
One Brow said: "Formal systems are not chosen for thoeries on how they apply, they are chosen for usefulness or general interest."
Well, there's a difference between initially framing the theoretical foundations of, say, math or plane geometry itself, and merely using an established formal system as an aid to understanding (explaining) a presumably empirical theory.
Einstein spent 8-10 years tryin to work out the math which would support and be consistent with notion of gravity and general relativity he had already conceived, theoretically. This was not a matter of Einstein having to go back 2000 years and re-invent a symbol for zero.
He had specific goals in mind, and carefully chose the mathmatical tools (presuppositions, and all) which would fit his theory. The final product was about as non-arbitrary as it can get.
I said: "This is all theoretical, of course, but the point is that the word "gravity" was simply coined (as were the words "two" and "three") to represent an abstaction made from observation."
I neglected to make one point I started out to make in this post, to wit: For the greeks, "gravity" was not some kinda "force," let alone one that universally applied to all matter. It was simply an inherent quality of certain kinds (but not all kinds) of matter. For centuries, the word "gravity" meant this. Did this conception of gravity "come from" falling apples? Is it something that can be "seen" in apples? I don't think so. Homey don't play dat!
Gravity is not a "fact," either, Gould's treatment of it to the contrary notwithstanding. You get the idea of what he's (Gould) trying to convey, but, strictly speaking, he's wrong. Falling apples are facts (data of the world), but not "gravity." Gravity, like evolution, is merely a mental abstraction.
You have some vague (to me) notion of what a "scientific theory" is.
A scientific theory is a collection of well-tested mechanisms and explanations regarding a phenomenon.
Do you see a "scientific theory" as being any kinda thought (which one might call "theoretical") about the objects of the world?
The objects of the world, as revealed by the results of experiements, are the facts to which theory pertains, the processes and mechanisms of the world, as revealed by experiements, are the contents, as we are using the word theory.
If you think that thoughts (inductive leaps) "originate" in experimental results, then it seems that you would have to agree that numbers "originate" in sense data too. We formulate the notion of "2" after first seeing 2 cows, then 2 pigs, etc., and then "processing" that data and abstracting the theoretical notion of 2. The numeral 2 is therefore in, and comes from, the world, not our brains.
That is why the concept is useful. However, the notion of a '2' has meaning divorced from any real context, and we even teach it this way. Natural selection has no meaning separate from a populations to act upon. I think you are conflating induction with inspiration.
You are arguing exactly the way a Platonist would for the "reality of," and the "origination of" numbers.
However, the Platonist wishes to make the abstraction into an real object. Natural selection is not an object.
Which is the same as saying the laws of logic are not required.
Not every logic has non-contradiction nor the excluded middle.
Without the strict application of logic, "scientific theory," at least in the sense that the wiki entry we reviewed defines and explains it, cannot exist. You might have "mystical" or "intuitive" theories without logic, but not "scientific theories."
I agree scientific theories need to incorporate some objective methodology of generating predictions based upon their contents, and that logic is the most common tool for this.
Why not?
It can be directly measured, for one thing, by the change in genetic content of a population.
It is not a full-blown "scientific theory," of course, but nor is it a "fact" which you can observe. It is a mental contruct.
In the usage "evolution occured", evolution is a fact, of the type Gould was referencing. If it were less strongly evidence, it would be a speculation, not a hypothesis.
But "gravity" is no more tangible than is the concept of the numeral 2. Neither comes from sense perception, per se, unless you are a Platonist, mebbe.
If gravity were not measurable, Newton's Law would never have existed.
Of course it is the same water, and it cannot be more or less than itself. That's just the old law of identity, right? Why can't the kid "see" this? Mebbe because the concept of "identity" is not an empirical one, cannot be seen, and is not "in" the water, at least not in any observable sense, whaddaya think?
Young children engage in magical thinking. However, if you mark the cup and the tube to the water reads'2 oz.' in both, the child will correctly read both numbers.
I gather that you are suggesting that scientific theories DO have a guarantee of correspondence to at least some part of the world. Are you somehow equating sense perception (one form of "fact") with scientific theory, thereby denying Gould's distinction?
No. I am equating the the use of observations of the world to being relevant to the world.
Einstein spent 8-10 years tryin to work out the math which would support and be consistent with notion of gravity and general relativity he had already conceived, theoretically. This was not a matter of Einstein having to go back 2000 years and re-invent a symbol for zero.
He had specific goals in mind, and carefully chose the mathmatical tools (presuppositions, and all) which would fit his theory. The final product was about as non-arbitrary as it can get.
The mathematical tools would be valid, though, even if the inductions of the theory were incorrect. Meanwhile, the inductions did not come from the mathematics, nor from arbitrary selection, but from induction on experiemental results.
One Brow said: "However, the Platonist wishes to make the abstraction into an real object. Natural selection is not an object."
I'm not sure why you say this, or exactly what you intend to mean. Not everyone who would be called a "platonist" these days rigidly adheres to every thing Plato said as true---kinda like with "darwinists"). That said, Plato never claimed that numbers, or any of his immutable "forms" were worldly objects. I don't think the distinction you're trying to make here is accurate. I know of no reason that Plato would not treat both natural selection and numbers in the same manner, whether that is to treat them both as "objects" or not.
Either way, you can't "refute" Platonism merely by denying it. You are free to claim that natural selection is not an "object," as you define objects, but unless you are using the term in the same way platonists do, you are merely stating your disagreement.
I said: "But "gravity" is no more tangible than is the concept of the numeral 2. Neither comes from sense perception, per se, unless you are a Platonist, mebbe.
You responded: If gravity were not measurable, Newton's Law would never have existed.
This totally ignores the point, for one thing (supposed "measurability" was not the issue), but even leaving that aside, it does not distinguish your epistemological view (which appears to correspond closely to what is often called "naive realism") from the platonic one. If numbers did not measure things, you would never be able to tell me that a standard basketball team has 5 players on the floor, either.
One Brow said: "[Evolution]can be directly measured, for one thing, by the change in genetic content of a population."
1. Many scientists now reject this as an adequate defintion of evolution. You can adopt it, if you choose, but, ya see, even there conceptual presuppositions are required before you can even start talking about what "the facts" show.
2. Of course the same is true of notions like "genetic content" and "population." These notions rest on imprecise abstractions and, in the case of the phrase "genetic content" in particular, are loaded with imported theoretical notions that are not self-evident (i.e., are not perceivale objects which "exist" in the world as "data").
If you think otherwise, then I wouldn't even know where to start to explain my (and many others') view on this topic. If you agree, then I think you are just missing the point.
This all stems from your claim that: "'Evolution occured' is not the type of knowledge that can be a hypothesis or theory."
You also attempt to defend this statement by suggesting that "If it were less strongly evidence, it would be a speculation, not a hypothesis." This strikes me as just another attempt to define "hypothesis" and "speculation" in an idiosyncratic way which somehow depends of the degree of "strong evidence." Either way, as I've said before, I'm not interested in semantics, per se. Is there something other than the "strength of the evidence," which distinguishes a hypothesis from speculation?
You also talk about the type of "fact" which Gould was referencing. My recollection that he distinguished theory from facts by saying facts were "data" and theories were "ideas." One of my posts specifically disputed the accuracy of his useage insofar as he referred to "gravity" (an idea) as a "fact," saying:
"Gravity is not a "fact," either, Gould's treatment of it to the contrary notwithstanding. You get the idea of what he's (Gould) trying to convey, but, strictly speaking, he's wrong. Falling apples are facts (data of the world), but not "gravity." Gravity, like evolution, is merely a mental abstraction."
You make no comment on this claim, but simply refer back to the "type of fact" Gould was referencing. As I read him, it is not really a "fact" at all, if one confines fact to "the data of the world," or however he put it. "Gravity" is not data, in my view. It is a theoretical construct.
Kant (and many others) made a basic distinction between two types of claims or truths, i.e. synthetic (empirical) claims about the world, and a priori claims, which could be analyzed and discussed without any reference to what is in the world whatsover.
This appears to be the distinction you are relying on, and it is a valid distinction. Not every claim is about what is "in the world." It's the conclusions you appear to draw from that distinction that I'm having trouble comprehending.
If you only mean that scientific theories "correspond to" the world in the sense that the subject matter is empircal, then, sure, who could disagree? But beyond that, so what?
The "correspondence theory of truth" basically assumes that a statement is "true" to the extent it "corresponds to" the actual world, as it truly exists. I have been taking you to mean "correspond" in this sense. I can't see where the premises of theoretical science are any more likely to "correspond to" the actual world than is the premise that "parallel lines will never meet." Again, I think we are talkng about premises, as opposed to a full explication of a particular theory that would consume many volumes of books.
On the general topic of "theorems" and formal deductive models in scientific theory, the "empirical" content of such, and the testability of, and evidence for, same, here are some (interspersed) excerpts from two websites:
"In population genetics, R. A. Fisher's fundamental theorem of natural selection was originally stated as:
"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."
The American George R. Price showed in 1972 that Fisher's theorem was correct as stated, and that the proof was also correct, given a typo or two[3] (see Price equation). Price showed the result was true, but did not find it to be of great significance....Price's equation is, importantly, a tautology. It is a statement of mathematical fact between certain variables...Due to confounding factors, tests of the fundamental theorem are quite rare.
http://en.wikipedia.org/wiki/Fisher's_fundamental_theorem_of_natural_selection
http://en.wikipedia.org/wiki/George_R._Price
While Price did not find the theorem to be of great significance, Fisher apparently believed it held "the supreme position among the biological sciences." The author here obviously uses the word "true" in the analytic, not synthetic, sense.
It was gittin a little fuzzy in my mind, so I re-read Gould's submission about fact and theory. http://www.stephenjaygould.org/library/gould_fact-and-theory.html
I was mistaken to say that he claimed "gravity" was a fact, which he clearly did not. In fact, he carefully distinguished falling apples from "the theory of gravity."
Gould does end up sounding equivocal, though, because he is trying to discuss two distinct aspects of "fact." First, he merely tries to define what facts consists of ("Facts are the world's data") in attempt to contrast the nature of facts with that of theories ("Theories are structures of ideas...").
Then he goes into a completely new notion about a fact, one of it's imputed qualities, which concerns the degree of subjective certainty which one attributes to what he is willing to call a "fact" ("In science, "fact" can only mean "confirmed to such a degree that it would be perverse to withhold provisional assent"). His immediate example of a "confirmed" fact goes straight back to the "data," falling apples, however ("I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms").
Nonetheless, many see to come away with the impression, as you did, that Gould is saying that "the theory of evolutiion is a fact" (insofar as "it would be perverse to withhold provisional assent"). He in fact says the opposite, but so many scientists seem to have tried to convey (without explicitly saying) that the theory is a fact, that I suppose that those used to listening to them think they already know what one is going to say before they even hear (or read) it.
I would not accuse Gould of any degree of deliberate equivocation, as I have NAS. I do think his analogy is inappropriate and misleading, though.
"Falling apples" are ideed in a category that I would call "data," but the same simply can't be said for "evolution." No one can directly perceive evolution as they can an apple. It makes some sense to compare the theoretical concept of "gravity" to "evolution" (as NAS does), because they are the same type of thing. But it makes no real sense to compare falling apples to evolution. As Gould himself noted, "ideas" are not "facts" in the sense that he is using the two terms, at least.
Another fallacious implicit "argument" from Gould about "creationism" is this: "I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms."
These scientists (Gould included, best I can tell) do not simply object to "equal time" being given to an alternative view. They seem to object to any suggestion that creationism or ID theory "could" possibly be true, or that such notions even exist as an alternative view, even if it would take less than 30 seconds to say it.
Would it be objectionable, pseudoscientific, and inappropriate to "cast doubt" on the theory of gravity by mentioning, in a physics class (without devoting "equal time" to the notion), that we can't be certain that the "law" of gravity will continue to apply in the future as it does now? I don't think Gould would make that claim. So why does he want to make it with respect to ID theory, I wonder?
That said, Plato never claimed that numbers, or any of his immutable "forms" were worldly objects.
Real objects, but not worldly, to my understanding.
I don't think the distinction you're trying to make here is accurate. I know of no reason that Plato would not treat both natural selection and numbers in the same manner, whether that is to treat them both as "objects" or not.
I don't know how Plato would have characterized processes, such as natural selection, or a mathematical example, addition. The reading I have done on mathematical philosophy so far says to me that processes are not treated as objects.
Either way, you can't "refute" Platonism merely by denying it.
I doubt it can be refuted at all.
I said: "But "gravity" is no more tangible than is the concept of the numeral 2. Neither comes from sense perception, per se, unless you are a Platonist, mebbe.
Going back, I disagree with there being no sense perception. When you hold an apple, your kinesthetic sense tells you your muscles are acting to keep it from falling. So, you do sense gravity.
This totally ignores the point, for one thing (supposed "measurability" was not the issue), but even leaving that aside, it does not distinguish your epistemological view (which appears to correspond closely to what is often called "naive realism") from the platonic one. If numbers did not measure things, you would never be able to tell me that a standard basketball team has 5 players on the floor, either.
In the phrase "5 players on the floor", the "5" is not an object and it is not being measured. "5" *is* the measure.
1. Many scientists now reject this as an adequate defintion of evolution.
There are scientists who claim that, when there is no change in heritable information evoltuion could still have occured? Or that, there was a change in heriable information, but no evolution occured?
2. Of course the same is true of notions like "genetic content" and "population." These notions rest on imprecise abstractions and, in the case of the phrase "genetic content" in particular, are loaded with imported theoretical notions that are not self-evident (i.e., are not perceivale objects which "exist" in the world as "data").
I think only a very reductionist frame of mind would say that information in genes ("genetic content") does not exist.
This all stems from your claim that: "'Evolution occured' is not the type of knowledge that can be a hypothesis or theory."
You also attempt to defend this statement by suggesting that "If it were less strongly evidence, it would be a speculation, not a hypothesis." This strikes me as just another attempt to define "hypothesis" and "speculation" in an idiosyncratic way which somehow depends of the degree of "strong evidence."
We agree (or so I thought) that facts and theories are different types of ideas. So, it is an attempt, perhaps idiosyncratic, to distinguish these types of ideas in their less-evidenced states just as we distinguish them in their heavily-evidenced states. Hypotheses can not become fact any more than theories can become fact, they are different types of data. Speculations can not become theories any more than facts can be theories.
You make no comment on this claim, but simply refer back to the "type of fact" Gould was referencing. As I read him, it is not really a "fact" at all, if one confines fact to "the data of the world," or however he put it. "Gravity" is not data, in my view. It is a theoretical construct.
I'm not going to pretend Gould is the ultimate authority. However, it is very clear that, to Gould, 'evolution occured' would be fact. He actually used "humans evolved" as an example of a fact that would not change while theories are debated.
Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts don't go away when scientists debate rival theories to explain them. Einstein's theory of gravitation replaced Newton's in this century, but apples didn't suspend themselves in midair, pending the outcome. And humans evolved from ape-like ancestors whether they did so by Darwin's proposed mechanism or by some other yet to be discovered.
I can't see where the premises of theoretical science are any more likely to "correspond to" the actual world than is the premise that "parallel lines will never meet." Again, I think we are talkng about premises, as opposed to a full explication of a particular theory that would consume many volumes of books.
Before we get too far into this question, can we agree the need to differentiate between a metaphysical premise of science that comes from no experiemntal results (such as uniformitarianism) and an empirical premise that results from an inductive leap (constancy of c)? Because I agree with you regarding the metaphysical premises and disagree on the empirical. Assuming we have risen to the level of fact/theory, the empirical premise will have been demonstrated through repeated testing, including for predictive power, within a specific environment, and is a least correspondent within that environment.
Nonetheless, many see to come away with the impression, as you did, that Gould is saying that "the theory of evolutiion is a fact" (insofar as "it would be perverse to withhold provisional assent"). He in fact says the opposite, but so many scientists seem to have tried to convey (without explicitly saying) that the theory is a fact, that I suppose that those used to listening to them think they already know what one is going to say before they even hear (or read) it.
You seem to be treating the statement 'In science, "fact" can only mean "confirmed to such a degree that it would be perverse to withhold provisional assent."' as a definition of the term fact. Rather, I submit it is a limitation. It comes within a paragparh that begins, 'Moreover, "fact" does not mean "absolute certainty." The final proofs of logic and mathematics flow deductively from stated premises and achieve certainty only because they are not about the empirical world.' I see Gould's statement as expressing a limit, not a definition. At no point does Gould deny a theory can be confirmed to that degree, he laments that evolutionary theory in general at that time was not so confirmed. However, he goes on to acknowledge that '... no biologist questions the importance of natural selection, ...'. Why would a theoretical construct go unchallened unless it was so confirmed that it would be perverse to withhold dissent? Scientists are not herd animals.
So, I don't agree that the degree of certainty is in any way connected to the distinction between fact and theory for Gould.
No one can directly perceive evolution as they can an apple.
A direct sense experience would be an observation. Facts can be non-observational. That is not idiosycratic usage.
Another fallacious implicit "argument" from Gould about "creationism" is this: "I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms."
These scientists (Gould included, best I can tell) do not simply object to "equal time" being given to an alternative view. They seem to object to any suggestion that creationism or ID theory "could" possibly be true, or that such notions even exist as an alternative view, even if it would take less than 30 seconds to say it.
Gould wrote this prior McLean vs. Arkansas. There were equal-time laws on the books in many states, and he is making a specific reference to them.
However, when high school students are studying disease, do you think phlogiston theory or Christian Science explanations merit even thirty seconds? How about flat earth theories in a geology class? Ptolemic astonomy in physics? I would rate any them as being equivalent to creationism.
As for ID, you are supposed to earn your time, even 30 seconds worth. Let them do 30 seconds worth of science, first.
Would it be objectionable, pseudoscientific, and inappropriate to "cast doubt" on the theory of gravity by mentioning, in a physics class (without devoting "equal time" to the notion), that we can't be certain that the "law" of gravity will continue to apply in the future as it does now? I don't think Gould would make that claim. So why does he want to make it with respect to ID theory, I wonder?
In one sense, the law of Gravity doesn't apply, it was replaced by general relativity. In another sense, it will always appply as long as we can hold to uniformitarianism, because as long as matter keeps acting the way it does today, the Law of Gravity will be a completely accurate estimation withing the measurement limits of a high-school course relying on unmechanized pendulums, stopwatches, and twisted wires.
However, that's beside the point with ID. The real problem with ID is that is has no scietific theory. It makes no predictions. It is a metaphysical proposition trying to dress itself up as science. It should no more be in a science classroom than materialsim should be.
One Brow said: "However, that's beside the point with ID. The real problem with ID is that is has no scietific theory. It makes no predictions. It is a metaphysical proposition trying to dress itself up as science. It should no more be in a science classroom than materialsim should be."
And I maintain that this is a bogus, hypocritical distinction. The Weismannian (neo-darwinist,) admittedly apriori, premise that there is, and can be, no "direction" to genetic variation is a metaphysical premise which makes no "predictions" either. It "predicts" (by fiat, not demonstration) that there can be no "lamarckian" variation. Design "predicts" that there is design, or some teleology in biological functions. What's the difference?
As Mayr said, and as I tend to agree, evolutionary theories boil down to 2 types:
1. Neo-darwinism, which excludes, as a fundamental presupposition, all possibility of direction or teleology, and
2. Theories, going by various names, which can be roughly, if not necessarily accurately, summarized under the rubric of "lamarckian," which posit some sort of "directionality," and active participation by the organism itself in the evolutionary process.
I have only read small portions of Gould's Structure of Evolutionary Theory, but what I have read is very interesting. Among other things, he details (and I do mean give elaborate and specific detail) about the formation and then what he calls the "hardening" of the modern synthetic theory of evolution.
This includes a determined effort at eliminating all "competing" theories and discipline (such as embryology) many of which had persisted for decades and still persist today in various forms. They were determined to discredit attempts at "pluralism" and to establish hegemony for natural selection, often on extremely dogmatic, a priori, grounds. Gould thinks a lot of this was done with an inadequate empirical basis and in the spirit of conquest and extermination, rather than objective science, and he exposes some of the "dirty tricks" used to accomplish the task.
You asked: "However, when high school students are studying disease, do you think phlogiston theory or Christian Science explanations merit even thirty seconds? How about flat earth theories in a geology class? Ptolemic astonomy in physics? I would rate any them as being equivalent to creationism."
My answer would be "yes, absolutely worth 30 seconds mention." The attempt to rip modern science from all of it's roots and history is NOT a good way to teach the subject generally in my opinion. Didn't we all hear in elementary school that people used to think the earth was flat, that the planets circled the earth, that mice were spontaneously generated from rags, etc.? That is not "teaching" the topic, as though it were current, accepted, science. There is no reason to say such topics are taboo and cannot be "taught" in the sense of even being mentioned.
Gould laments what he called the "dangerous overconfidence" of the neo-darwinists and the suppression of views which (Gould believes) had substance. He notes that what is resisted as a "competing" theory in one generation is, once conquered, no longer even mentioned to the next generation of scientists, with the "teachers" basically pretending as though such alternative theories (and the evidence they were founded upon) never really existed at all in any meaningful sense.
It is the very attempt to exclude all competing viewpoints which I find so objectionable. I see nothing inherently "religious" in ID theory. Nor do I see it as inherently "supernatural," by any means. One can posit a supernatural agent as the "designer," but that is by no means required. In my view (echoed by Woese and many others), neo-darwinism demanded a commitment to very narrow view of what is "real," what is "possible," what types of explanations are "acceptable" and what types of questions are even "meaningful." So narrow as to render it virtually impotent in trying to answer certain fundamental questions. Popper said it was a theory of genetics, whereas as what was needed was a theory of form. Neo-darwinism does not even attempt to answer fundamental questions about how new variation and new information arises. It simply presupposes that it is, and will be, there there while dogmatically insisting that it arises by "capricious" and totally undirected means.
Do you have any comment on Fisher's position that his mathematical tautology occupied the "supreme position" amongst "laws" in the biological sciences? I mean, they say it can't even be tested, due to confounding factors. What is "empirical" about this approach?
One Brow said: "Assuming we have risen to the level of fact/theory, the empirical premise will have been demonstrated through repeated testing, including for predictive power, within a specific environment, and is a least correspondent within that environment."
Well, no, we disagree here. There is no such thing as an "empirical" premise that I can see. A fundamental theoretical premise cannot be empirical, by definition (at least as Asimov defines a "premise" or "assumption").
Let me try an example to explain what I'm trying to say. Is it an "empirical fact" that the sun rises in the east and sets in the west? I'm sure you would say, "no, not literally" in response. Yet in a certain sense, and from a certain viewpoint, that is indeed a "fact." But it is NOT an purely empirical fact. It is sense perception interpreted by conceptual categorization and analysis, which themselves contain certain presuppositions.
Prediction, per se, is wholly inconclusive, and can arise from the mere tautological application of our conceptual categorization. Let's say my "theory" is that Mercury gets up early every day, hitches up his sky-ridin team of horses, and drags the sun from horizon to horizon. Well, every time the sun "rises" and "sets" this "confirms" my theory. Potentially limitless "theories" could be conceived which would be "consistent with" observation (witness ptolemic astronomy, for example). Do the "empirical facts" show any of these to be necessarily reliable or "true?" Do those theories come from the facts themselves? No, of course not. They are products of human imagination. The fact that I am trying to explain empirical phenomena does not make my premises "empirical."
I said: "But "gravity" is no more tangible than is the concept of the numeral 2. Neither comes from sense perception, per se, unless you are a Platonist, mebbe.
Going back, I disagree with there being no sense perception. When you hold an apple, your kinesthetic sense tells you your muscles are acting to keep it from falling. So, you do sense gravity.
Naw, you sense that your muscles are acting (maybe, not sure), you do not sense "gravity." You might invent a notion, which you nominate (call) "gravity" to go with this association. But what is it? A natural desire to descend, inherent in the object? An external force? Curved space? What ever you decide to say it is, it is a mental construction, not something "in" the object which you observe or otherwise sense. It is a deriviation from sense perception, not sense perception itself.
One Brow said: "In the phrase "5 players on the floor", the "5" is not an object and it is not being measured. "5" *is* the measure."
Heh. Well, naw, I would say that the counting to 5 is the "measuring," and that the numeral 5 is the result of the measuring, not the measure itself. Of course 5 is not an object, the team is the "object." Furthermore, if you're relying on "arbitrary" formal numerical systems to supposedly "measure" natural selection (which can't "really" be done, if you're relying Fisher's fundamental theorem, anyway), then you're no longer dealing with "empirical" matters, are you?
I don't know much about it, but I gather that there was (and still is) intense and extended debate about whether any given genetic change was a result of selection or merely neutral drift. If you can't even identify natural selection with certainty, how can you "measure" it with certainty? It's not like measurin the length of the tail of a rat before you chop it off, ya know?
But, all funnin aside, I really think it's irrelevant to the point that I was trying to make.
One Brow said: " Hypotheses can not become fact any more than theories can become fact, they are different types of data. Speculations can not become theories any more than facts can be theories."
Well, your conclusion is your premise, and your premise is your conclusion. You have concluded that the claim that "evolution occurred" is a "fact," following Gould's attempt to define it as such. I say it aint no fact, not if "fact" is defined as the data of the world.
I don't have a practical problem with calling it a "fact," but it is not data. It is an interpretation of data, based on deductions, hypotheses, undisclosed premises, etc. Another interpretation of the data is that God created every fossil, etc., for sport, and that evolution never occurred.
One Brow said: "At no point does Gould deny a theory can be confirmed to that degree, he laments that evolutionary theory in general at that time was not so confirmed. However, he goes on to acknowledge that '... no biologist questions the importance of natural selection, ...'. Why would a theoretical construct go unchallened unless it was so confirmed that it would be perverse to withhold dissent?"
Well, because you yourself have emphasized that facts are not theories, and that the degree of certainty is not the issue as to whether a fact can be a theory. Yet the confusion persists.
With respect to evolution in particular Gould says: "Evolutionists have been clear about this distinction between fact and theory from the very beginning, if only because we have always acknowledged how far we are from completely understanding the mechanisms (theory) by which evolution (fact) occurred." I would expect leading scientists in any other discipline to say the same about their specialty. Facts (data) are "confirmed" by raw observation. The "confirmation" process for a theory is of an entirely different nature and order. Of course, any given individual is free to be as subjectively "certain," to the point of asserting that a given theory is absolute immutable fact, as he chooses to be. That, though, is a separate issue from "confirmation."
As far as natural selection goes, the putative agreement about it's "importance" should not be confused with agreement about it's role in causing evolution (which is what the theory is about).
The point I was making in the last paragraph of the last post is one that I think Gould himself makes quite clear in the full context of his musings upon the "importance" of natural selection, which you stripped from it's context:
"The fruitful theoretical debate that Darwin initiated has never ceased. From the 1940s through the 1960s, Darwin's own theory of natural selection did achieve a temporary hegemony that it never enjoyed in his lifetime. But renewed debate characterizes our decade, and, while no biologist questions the importance of natural selection, many doubt its ubiquity."
And that's putting it very mildly. The numerous "doubts" about the role of natural selection is causing evolution go far beyond the mere question of it's "ubiquity."
Part of the response will be in the discussion on evoution thread.
You asked: "However, when high school students are studying disease, do you think phlogiston theory or Christian Science explanations merit even thirty seconds? How about flat earth theories in a geology class? Ptolemic astonomy in physics? I would rate any them as being equivalent to creationism."
My answer would be "yes, absolutely worth 30 seconds mention." The attempt to rip modern science from all of it's roots and history is NOT a good way to teach the subject generally in my opinion.
That's quite the equivocation. I have no objection to creationism being introduced as a historical concept of what people used to believe before we learned better. However, that is not the point to which I was responding. As a reminder, your point was, 'These scientists (Gould included, best I can tell) do not simply object to "equal time" being given to an alternative view. They seem to object to any suggestion that creationism or ID theory "could" possibly be true, or that such notions even exist as an alternative view, even if it would take less than 30 seconds to say it.'
So, we are not talking about the concept of a flat earth, alchemy, or phlogiston as a historical point of view no longer tenable. We are talking about it being mentioned as an alternative point of view, being granted as legitmate with the knowledge we have today. Should we teach high-school kids that some people believe in a flat earth, and that it's just another point of view?
One Brow said: "Assuming we have risen to the level of fact/theory, the empirical premise will have been demonstrated through repeated testing, including for predictive power, within a specific environment, and is a least correspondent within that environment."
Well, no, we disagree here. There is no such thing as an "empirical" premise that I can see.
You don't understand the difference, or you think the difference is misleading? If the latter, why?
A fundamental theoretical premise cannot be empirical, by definition (at least as Asimov defines a "premise" or "assumption").
Let me try an example to explain what I'm trying to say. Is it an "empirical fact" that the sun rises in the east and sets in the west? I'm sure you would say, "no, not literally" in response. Yet in a certain sense, and from a certain viewpoint, that is indeed a "fact."
I agree with your last sentence.
But it is NOT an purely empirical fact. It is sense perception interpreted by conceptual categorization and analysis, which themselves contain certain presuppositions.
So, can we call that an observation, for short?
Prediction, per se, is wholly inconclusive, and can arise from the mere tautological application of our conceptual categorization. Let's say my "theory" is that Mercury gets up early every day, hitches up his sky-ridin team of horses, and drags the sun from horizon to horizon. Well, every time the sun "rises" and "sets" this "confirms" my theory. Potentially limitless "theories" could be conceived which would be "consistent with" observation (witness ptolemic astronomy, for example). Do the "empirical facts" show any of these to be necessarily reliable or "true?" Do those theories come from the facts themselves? No, of course not. They are products of human imagination. The fact that I am trying to explain empirical phenomena does not make my premises "empirical."
When you use the mechanism just to explain past data, it is not a theory at all. It's still a hypothesis. Your Mercury theory is not confirmed until you can use it to make predicitons that are different from other theories, and have *those* predictions be verified. Einstein's special relativity, and general relativity, were initially hypotheses. they became theories after they were able to not only explain what other theories had not, but also make predictions other theories did not, and see those predictions verified. I agree that a tautological construction or a just-so story that creates no new ideas for experiments, offers no new ways to test itself, and says what every other idea says and no more is not a theory.
Naw, you sense that your muscles are acting (maybe, not sure), you do not sense "gravity." You might invent a notion, which you nominate (call) "gravity" to go with this association. But what is it? A natural desire to descend, inherent in the object? An external force? Curved space? What ever you decide to say it is, it is a mental construction, not something "in" the object which you observe or otherwise sense. It is a deriviation from sense perception, not sense perception itself.
If you care to parse it that finely, OK.
One Brow said: "In the phrase "5 players on the floor", the "5" is not an object and it is not being measured. "5" *is* the measure."
Heh. Well, naw, I would say that the counting to 5 is the "measuring," and that the numeral 5 is the result of the measuring, not the measure itself.
You mean, you are measuring verbal utterances or some such thing? OK.
Furthermore, if you're relying on "arbitrary" formal numerical systems to supposedly "measure" natural selection (which can't "really" be done, if you're relying Fisher's fundamental theorem, anyway), then you're no longer dealing with "empirical" matters, are you?
I agree that natural selection can't be measured in that manner, regardless of Fisher's fundamental theorem. Of course, natrual selection is not a fact, so that is not surprising.
One Brow said: " Hypotheses can not become fact any more than theories can become fact, they are different types of data. Speculations can not become theories any more than facts can be theories."
Well, your conclusion is your premise, and your premise is your conclusion. You have concluded that the claim that "evolution occurred" is a "fact," following Gould's attempt to define it as such. I say it aint no fact, not if "fact" is defined as the data of the world.
There is obviously a difference between your useage and Gould's.
I don't have a practical problem with calling it a "fact," but it is not data. It is an interpretation of data, based on deductions, hypotheses, undisclosed premises, etc. Another interpretation of the data is that God created every fossil, etc., for sport, and that evolution never occurred.
Yes, indeed. Of course, that position does violate the unproven, metaphysical assumption of uniformitarianism, so it is not a scientific position, and therefore not one that science can prove or disprove.
As I understand him, Kant argues that we are justified in feeling very "certain" about some of our fundamental "categories of perception," such as space, for example. He does not, however, argue that we are justified in believing that such concepts actually exist, "out there." We are certain of them only because we can perceive things no other way, he says. We are certain that we "perceive" things with the category of "space" as a necessary component of our perception, that's all. And, as the old greek sophists agrued, sense perceptions are (for the person experiencing them) direct and indisputable.
I can feel confident that (what I refer to as) "matter" exists. That said, the very concept of "matter" is just that, a concept, a "theoretical construct." The whole notion tends to becomes very vague in quantum physics, for example.
One Brow said: So, we are not talking about the concept of a flat earth, alchemy, or phlogiston as a historical point of view no longer tenable. We are talking about it being mentioned as an alternative point of view, being granted as legitmate with the knowledge we have today. Should we teach high-school kids that some people believe in a flat earth, and that it's just another point of view?"
Well, sure, my answer would be the same. To be fair, if one is going to present it as something people still believe, their grounds for doing so should also be summarized, and not just ridiculed. Greeks has many "good reasons" for believing that the earth was motionless. They were not simply utter fools.
I really don't even follow these court cases about the teaching of evolution in schools. That said, it is my understanding that the Dover (or some other recent) case was all about the insertion into biology texts a statement to the effect that the currently promulgated theory of evolution is not a "certain fact" and that there are certain "gaps" in the theory.
I don't think any legit scientist would actually deny these propositions, and yet, as a group, they seem to feel that such admissions should not be uttered in the presence of impressionable teenagers at school, and that protracted litigation is necessary and desirable to prevent that from happening.
Wiki says the Dover case was over whether this brief statement should be read to high school students:
"The Pennsylvania Academic Standards require students to learn about Darwin's theory of evolution and eventually to take a standardized test of which evolution is a part.
Because Darwin's Theory is a theory, it is still being tested as new evidence is discovered. The Theory is not a fact. Gaps in the Theory exist for which there is no evidence. A theory is defined as a well-tested explanation that unifies a broad range of observations.
Intelligent design is an explanation of the origin of life that differs from Darwin's view. The reference book, Of Pandas and People is available for students to see if they would like to explore this view in an effort to gain an understanding of what intelligent design actually involves.
As is true with any theory, students are encouraged to keep an open mind. The school leaves the discussion of the origins of life to individual students and their families. As a standards-driven district, class instruction focuses upon preparing students to achieve proficiency on standards-based assessments."
This statement "teaches" nothing about intelligent design, although it does provide access to a textbook IF they should desire a better understanding of it's claims. What's the big problem?
That rather innocuous statement, says, as I read it, that the schools will NOT teach ID theory (class instruction will focus on proficiency in "standards-based"--which purportedly includes darwinism, but not design--assessment, and discussion of such issues will be left to "individual students and their families").
What is this fight really about? Scientists also want to prevent discussion of ID by students with their families, too, that it? Is the goal "education," or indoctrination? Students should not be allowed to "keep an open mind" about all theories (including ID theory)?
What is it about any part of this brief statement that leads scientists to believe that high school students should not be allowed to even hear it? Would any reputable scientist really try to claim that "Darwin's theory" is not a theory, but rather a fact?
The statement may go a little too far in asserting that there is "no" evidence for certain aspects of darwinian theory, because there is always some "evidence" for just about anything (including God), depending on interpretation. But would they really dispute the contention that there is no compelling evidence for the claim that gradualism and the known mechanisms of micro-evolution amply support the contention that such premises and mechanisms "explain" macroevolution (for just one example of the possible "gaps" the statement might be referring to)?
If it is simply the "no evidence" portion that they find objectionable, why didn't their lawsuit simply try to correct that? What is their opposition "really" all about, I wonder?
ID stuff responded to in the other thread.
I can feel confident that (what I refer to as) "matter" exists. That said, the very concept of "matter" is just that, a concept, a "theoretical construct." The whole notion tends to becomes very vague in quantum physics, for example.
By that standard, you can't say it is a fact that Washington was the first US President, either. It's not how scientists use teh term, or most people.
To be fair, if one is going to present it as something people still believe, their grounds for doing so should also be summarized, and not just ridiculed.
Would it be fair to distinguish the actual reasons from the pseudo-scientific claims often put forth by, for example, falt-earthers? Would it be fair to point out that they misuse science instead of using it? Woould it be fair to point out that their speculations and hypotheses have failed every attempt at novel predictive testing?
Greeks has many "good reasons" for believing that the earth was motionless. They were not simply utter fools.
In fact, it would do a disservice to them to hold to their ideas for foolish reasons, or using foolish and deceptive justifications. I don't find 'they didn't have the tools to understand it correctly' to be any indication of follishness on their part.
A slight rewording of the Dover statement would be:
"The Theory is not a fact. Gaps in the Theory exist for which there is no evidence. A theory is defined as a well-tested explanation that unifies a broad range of observations.
Various established religions offer explanations of the origin of life that differ from Darwin's view. The school library contains a variety of materials that elaborate upon various religious views and these are available for students to see if they would like to explore such views in an effort to gain an understanding of what they actually involve."
Would this be the "establishment of religion?" Would it constitute a failure to separate church and state? I can't see how. Is the mere acknowledgment that religious views exist forbidden?
I am not conceding that ID is synonymous and co-extensive with "religious views," because I don't think it is, by any means. My point is simply that, even if it were, what's the big deal? Why are scientists so defensive about their precious "theory of evolution?" Why the need to try to pre-emptively eradicate the consideration of religious views by high school students?
Parents can try to instill a religious outlook in their children if they choose. They can endeavor just as diligently to instill an atheistic outlook, too. Either way, you would hope that, at some point, the children re-evaluate their indoctrination on such matters, and decide for themselves, based on their own individual experiences, understandings, etc., what they feel is worthy of belief.
Some of these militant atheists are just as evangelical and as imbued with dictatorial ambitions (regarding beliefs) as any fundie could be. How can I approve of their tactics while disapproving of the same tactics from religious folk? Only one way: To not give a damn about censorship or indoctrination, at least not if it furthers my own personal view. In other words, I can approve only if I am as fanatical and partisan as they are.
A slight rewording of the Dover statement would be:... Would this be the "establishment of religion?" Would it constitute a failure to separate church and state? I can't see how. Is the mere acknowledgment that religious views exist forbidden?
Part of the requirement for such statements would be that they serve a valid secular purpose. You could make the purpose valid and secular by having it say, for example, "Various established religions offer explanations of the origin of life that differ from Darwin's view, but on the points where they make different predicitons from modern evolutionary theory, they are incorrect, and on the points where they do not, they are not relevant scientifically." However, a school board that would make that statement would probably not make a Dover statement at all.
I am not conceding that ID is synonymous and co-extensive with "religious views," because I don't think it is, by any means. My point is simply that, even if it were, what's the big deal?
Neither religion nor atheism belongs in the public schools.
Why are scientists so defensive about their precious "theory of evolution?"
Decades of distortions, lies, and character assasinaitons.
Why the need to try to pre-emptively eradicate the consideration of religious views by high school students?
You think public schools should teach religion as being true?
How can I approve of their tactics while disapproving of the same tactics from religious folk?
I don't know of any American atheist that supports teaching atheism in schools, and certainly none of the major names do. That's the difference.
1) Pandas and People is a text full of pseudo-scientific objections and ill-founded attacks on evolutionary theory. ASSUMING THAT'S TRUE, WHICH I DON'T, SO WHAT?
So there is no valid, secular purpose to mention it in a class; it can only do harm.
2) Intelligent design is not science, and doesn't need to be brought into a science class. THEY ARE KEEPING IT OUT OF THE SCIENCE CLASS, THEY SAY.
The announcement, which specifically endorsed the book, was in biology class.
3) The reason for reading the statement is to cast doubt on evolutionary theory specifically. No one went into physics classes to promote books on Ptolemic astronomy. YEAH, SO?
If they choose only one theory to single out for the "not a fact" propaganda, it provides official sanction to treating that theory as different from other scientific theories.
4) The school board was acting with very specific religious goals in mind. ASSUMING THAT'S TRUE, SO WHAT? DOES THE BRIEF STATEMENT SAY ANYTHING ABOUT RELIGION?
Purpose is one of the prongs of the Lemon test.
5) The statement tries to indicate that the status of theory means evolution can't be certain, which is false. HOW DOES IT "TRY TO INDICATE" THAT?
If you don't see that in the statement, fine. It was plain to me.
Well, assuming that's true, then if any student wanted to read it, I guess they would see that.
Most high school students don't have our background or interest in the question or theory vs. fact.
Or should all so-called "religious" books be banned from school libraries too, ya figure?
I have no objection to any religious or philosophical work (such as Pandas and People) being in the library. I would object to any statement in the classroom recommending the students read such a book.
My point about the dark matter thing is probably obvious, but can you see how much of "scientific theory"
While the wikipedia entry carelessly (if technicallyh correctly) refers to the study of dark matter as "dark matter theory", the opening sentence is very careful to not say the use of dark matter is a theory. Note how different that is from the opening sentence of atomic theory, for example. There is no theory of dark matter.
One Brow said: "I'm not claiming that is the whole story, of course, but what is left unexplained, to you?"
The question is about the development of highly complex, highly interdependent information, all of which seems to serve teleological ends.
At each step, the information comes from the random addition information to very slightly less complex, highly interdependent information selecting with a very high tolerance for failure.
By "randomly making changes" in that post, I mean adding nothing, just changing the arrangement of the existing hardware. Of course, the changes in the available software would need to be explained too.
Of course, evolutionary theory does have ways to add both hardware (gradual subdvision of one piece into two is one method) and software (again, gene duplicaiton is one method).
I mean, like, if I start with a bacterium, and then just started rearranging the gene sequences, could I expect to eventually turn it into a whale, without adding information, ya think?
How many generations do you plan on alloowing yourself? How many different mechanisms will you put into play? What is the limit to the amount of change you can generate? If you can't set a limit, how can you say any specific amount is too much? Why can't you eventually get something whale-like?
I see it as precisely the opposite. Lewontin has already informed us that it is a "fact" that all life comes from life. Abiogensis would be a gross, one-time (well, maybe thousands of times, but, either way) violation of that "law." That aint uniform operation of the law, is it?
Actually, Lewontin's "fact" woulde be that when life is present, more life can only come from existing life.
I suspect that you are being "uniformitarian" in your devotion to the premise that blind mechanistic, forces, acting on matter in motion in the void, "created" all that there is,
No, that's a faith position that I hold by faith. We have no evidence either way.
Simplistic examples like the one I'm about to give have no doubt been advanced thousands of times, but I don't feel like looking for a ready-made example, so...What it will not do is turn into a copy of "War and Peace." To begin with, it's just not long enough. I would have to add a whole bunch of paragraphs to the original, at a very minimum. That would not be mere "variation," it would be the creation of entirely new information. An imperfect xerox machine can't add that.
What the imperfect xerox machine occasionally copies a paragraph, or even the entire page, a second time onto the same sheet? It can eventually get as long as War and Peace then. What's to stop it from becoming any book if that book if favored by a selection process?
The statement that something is "supernatural" is empty of empirical content and merely reflects one's ontological (pre-)judgment. It serves to express the brand of metaphysics which the speaker adheres to.
OK. However, since the position of the two primary types of ID is to disallow the creation of information by natural, undirected means, your understanding o fsup-ernatural does not change the inevitable conclusions of their arguments.
Although we (mostly I) have made many pages of posts on "evolution," that has not really been my topic of main interest at any time. We have also discussed epistemology, the philosophy of science, authoritarian indoctrination of belief systems, dogmatism, etc., which are all actually of more interest to me.
I enjoy these discussions as well.
Anyway, back to dark matter for a second.
I agree the use of dark matter is not a theory and the existence of dark matter is not a fact (speaking scientifically). However, I('m not aware of a source that says it is either.
But, if 3/4 of the matter in the universe is dark matter, and if it is undetectable, why would we think Newton's formula is accurate?
The metaphysical assumption of uniformitarianism. Newton's formula works for ouur galaxy and a few others, but not for many/most of them.
The point is, again, that your mathematical formulas are only as good as the assumptions used to derive them.
Newton's Law was not based on assumpitons, but on an inductive leap based upon experimental results, including experiements where it was directly tested with masses supported by twisted wires.
So, ya can't calculate a formula for gravity, if ya have dark matter. We do have dark matter. Therefore our formula for gravity can't be formulated. But, wait, it's our formula for gravity that tells us we have dark mattter....hmmmm.
The theory is an extrapolation or an empirically verifiable local phenomena, as all theories are or become.
These guys will come up with any and every kinda new, exotic "particle," never seen by anyone, to "explain" just about every contradiction their theory generates, ya know?
None of those speculations are given the status of facts until they are tested and verified.
This is the point I was making after reading the website you referred me to, where some blogger was using a mathematical theorem to "prove" that random mutations can add "new" information. Although the word "new" is often used to designate a mere substitution or difference (e.g.: "I just got a new truck, it's a '49 Hudson"), that is not "new" is the sense of newly created. Even though my car is then different, it is not really a "new" car just because I replace the worn-out floormats, either.
Information is not a physical commodity like a floormat.
Woese and two colleages from the Physics department at the U of I, claim that the universality of the genetic code can NOT be explained (as hence could not be "evidence for") by common descent.
We have a variety of slightly different codes to examine. Is there any evidence any of these codes are more efficient?
What exactly serves as "evidence" for common descent? Well, just about anything, if you already know that common descent is a fact, I spoze. Like similar kinda teeth in a dog and a whale, for example, ya know?
Do you feel Theobald's 30 lines of evidence are all circular?
With the exception of minor deviations occasionally discovered, the same DNA code is found in all species. And that code is so efficient it is sometimes labeled as “optimal.”
Optimal compared to other possible DNA codes? I disagree. Neither the DNA hardware nor the DNA coding is particularly optimal.
But while evolution must be very adept at creating new codes, it must paradoxically also be unable to create new codes. The code must be frozen, otherwise it would not be universally shared amongst the species.
He just acknowledged it was not quite universal. Self-contradictions don't make for a convincing argument.
If the code is so difficult to evolve these days, why was it so easy to evolve back then?
Because it exists now, and did not exist then.
Whoops, I lost track of the thread I was in. Sorry.
One Brow said: "Information is not a physical commodity like a floormat."
No, it's not. That's the point. It's not like hydrogen and oxygen atoms, either. Putting the two together may get you a different, ya might even say "new," substance, like water, but it won't add any new information to anything. Where does the new information come from. Saying that it comes "gradually" (which always seems to be the magical bean for darwinists) doesn't address the question at all, it just ignores it.
One Brow said: "Do you feel Theobald's 30 lines of evidence are all circular?"
I don't know them and that wasn't the topic I brought up. You had said earlier that you thought the near-universal genetic code was one of the strongest proofs for common descent.
Woese and others say it can't be evidence for common descent, because it could not have arisen via common descent. A theist could easily claim that the near universality of the code is proof that it was created by God. Why not believe that? Common descent doesn't explain it.
Like I said before, everything will provide evidence for something you already know to be a fact. PBS has no trouble saying that some ancient dog fossil proves "for certain" that it was the ancestor of the whale. But that can only be because it already knew it, before the dog bone was found. The dog bone certainly didn't prove it.
For the Marxist, every event that occurs just provides further proof of the truth of Marxism. For the Freudian, every act that occurs just provides further proof of the Freud's psycholanalytic theory. For the darwinist......
Neo-darwinism simply assumes that virtually infinite variation will become available by random copying errors, etc. It's, like, a joke, ya know? It's like if I needed to get around faster, "evolution" would find put a carburator on my porch, then an axle, then a steering wheel, etc., until I had all the parts to build a car from scratch. Course, I wouldn't know what to do with them parts, so "evolution" would have to give me blueprints, socket wrenches, hoists, and all kinda other stuff for me to know how to, and be able to, make a car outta them parts. Well, actually, it's kinda like evolution just delivered a car to my driveway. Next thing I need--a computer. Should be here any ole time, I spect. Everything I need always is--it just kinda "appears," ya know?
I been thinkin that I need a tail, about 2 feet long, growin outta the back of my neck to I can clean and scratch my back easier. It may be too late for me, but, now that I've identified the need, I spoze my next chile will have one. A couple more generations, and every person on the planet will have one, because it will be an "advantage," ya know?
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